Duty Cycle & PWM Calculator

A periodic signal — a square wave, a PWM drive signal, a pulsed radar transmission, an intermittently-running compressor — repeats itself every fixed interval, the period. Within each period, the signal is "on" for some portion of the time and "off" for the rest. Duty cycle simply measures what fraction of that period is spent on, regardless of how intense the "on" state actually is.

Choosing a PWM switching frequency: the switching frequency (how fast the on/off cycle repeats) is a separate design decision from duty cycle, and picking it involves real trade-offs. Too low, and an LED driven by PWM can visibly flicker, or a motor can audibly whine or vibrate as it responds to individual pulses rather than a smooth average; many LED dimmers therefore switch well above roughly 200–500 Hz (often into the low kHz range) specifically to stay above the range of visible flicker and audible motor noise. Too high, and switching losses in the driving transistor rise (each on/off transition itself dissipates a small amount of energy, and more transitions per second means more of this loss), while the drive electronics also need to be fast enough to produce clean edges at that rate. Typical PWM switching frequencies range from a few hundred hertz for basic heater or valve control, through the low kilohertz range for LED dimming and small motor drives, up to tens or hundreds of kilohertz for switch-mode power supplies and motor drives using MOSFETs, where minimizing inductor/capacitor size favors a higher frequency.

Resolution — how finely duty cycle can actually be set: a microcontroller's PWM output isn't continuously variable; it's stepped, because duty cycle is set as a count of timer ticks out of a fixed total (for example, an 8-bit PWM timer can only represent 256 distinct duty-cycle steps, giving roughly 0.39% resolution per step). A higher-resolution timer (10-bit, 16-bit) allows finer duty-cycle steps, which matters for applications like precise motor speed control or smooth LED dimming curves where a visible "stepping" between adjacent brightness or speed levels would otherwise be noticeable. Resolution and maximum achievable switching frequency are often linked for a given timer clock speed — requesting a higher PWM frequency from the same timer clock typically reduces the number of achievable duty-cycle steps, and vice versa.

Duty Cycle Formula (From Time)

D (%) = (PW ÷ T) × 100%, where PW is the pulse width (on-time within one cycle) and T is the period (total time of one complete cycle). Expressed as a plain ratio rather than a percentage, this same value is the duty factor: df = PW ÷ T. Since period and frequency are reciprocals (T = 1 ÷ f), duty cycle can equally be written as D (%) = PW × f × 100%, with PW in seconds and f in hertz.

Duty Cycle Formula (From Power)

D (%) = (P̄ ÷ Pp) × 100%, where P̄ is the average power over a full period and Pp is the peak (pulse) power. This form is especially useful when the underlying pulse timing isn't directly measurable but average and peak power readings are — a common situation in pulsed RF, radar, and laser systems. It follows directly from the time-based definition, since average power is just the peak power scaled down by the same fraction of time the signal is actually on.

Pulse energy: once both a power value and a timing value are known, the energy delivered in a single on-pulse can be found from Ep = Pp × PW, or equivalently Ep = P̄ × T — the two expressions give the same answer because P̄ = D × Pp and T = PW ÷ D cancel out identically.

Worked example (time-based): an NE555-style oscillator produces a period of T = 1 s, with the output high for PW = 225 ms = 0.225 s. Duty cycle D = (0.225 ÷ 1) × 100% = 22.5%, duty factor df = 0.225, and the equivalent frequency is f = 1 ÷ T = 1 Hz.

Worked example (power-based): a pulsed radar transmitter is on for 10 ms out of every 1000 ms (1 s), giving D = 1%. If its peak transmit power is 20 kW, the average power over that period is P̄ = D × Pp = 0.01 × 20,000 W = 200 W, and the energy per pulse is Ep = 20,000 W × 0.010 s = 200 J.

Solving in reverse — from a target duty cycle to average voltage: the most common real-world question isn't always "what's my duty cycle" but the opposite: "I want to run this motor/actuator at a given duty cycle at a given switching frequency — what average voltage and ON/OFF timing does that actually give me?" This calculator's "D% → Voltage" mode handles that direction directly: enter the desired duty cycle, the switching frequency (or period), and the supply voltage, and get period, ON time, OFF time and Vavg ≈ (D÷100) × Vin back out. Worked example: a 24 V linear actuator driven at 75% duty cycle, 1 kHz switching — period T = 1÷1000 = 1 ms, ON time = 0.75 × 1 ms = 0.75 ms, OFF time = 0.25 ms, and Vavg = 0.75 × 24 V = 18 V. Halving the duty cycle to 37.5% would roughly halve the average voltage the actuator sees, which is the basic mechanism behind PWM speed control.

Why time units matter: pulse width and period must be converted to the same time base before dividing — mixing milliseconds with seconds without converting first is one of the most common sources of a wrong duty-cycle result. This calculator converts every time and frequency entry internally to a common base (seconds and hertz) before computing, regardless of which units you type each value in.

Choosing period vs. frequency as an input: some datasheets and oscilloscope readouts quote period directly; others quote frequency. Both describe the same underlying timing, so this calculator accepts either — enter whichever one your source data actually gives you, and the other is derived automatically (T = 1 ÷ f).

1. Treating duty factor and duty cycle as different quantities. They are the same ratio — duty factor is simply duty cycle expressed as a decimal (0 to 1) instead of a percentage. Confusing the two commonly leads to a value that's off by a factor of 100.

2. Mixing time units before dividing. Entering pulse width in milliseconds and period in seconds without converting both to the same base first silently produces a duty cycle that's off by orders of magnitude — always convert to a common unit (or let the calculator do it) before computing PW ÷ T.

3. Entering a pulse width greater than the period. A valid PWM signal cannot be "on" for longer than one full cycle — if PW exceeds T, the parameters describe an impossible signal and should be rechecked rather than accepted as a duty cycle above 100%.

4. Treating Vavg = D × Vin as the actual load voltage rather than an ideal-waveform average. This formula gives the average of an ideal, lossless 0-to-Vin switched waveform — actual buck converters, motor drives, and LED dimmers have switching losses, semiconductor voltage drops, and ripple that make the measured average somewhat different from this ideal figure, particularly at low duty cycles.

5. Confusing average power with peak power in a pulsed system. A radar or laser system's headline "power" rating is often peak power, which can be many times the actual average power the system dissipates or radiates continuously — using peak power where average power is required (for thermal or energy-cost calculations) significantly overstates the real figure.

6. Ignoring a device's rated maximum duty cycle. A welder or compressor rated for, say, 60% duty cycle over a 10-minute window is not rated for continuous 100% operation — running it beyond that rating for sustained periods risks thermal damage or a protection cutout, even if each individual "on" period seems short.

7. Forgetting that pulse energy needs both a power value and a timing value. Ep = Pp × PW (or P̄ × T) cannot be found from power alone, or from timing alone — at least one power quantity and one timing quantity (period, frequency, or pulse width) must both be known.

8. Confusing PWM switching frequency with any other frequency in the same system. A motor's electrical PWM switching frequency (say 16 kHz) has no direct relationship to its mechanical rotation speed, and an inverter's SPWM carrier frequency is not the same as its synthesized output frequency (typically 50/60 Hz) — treating these as interchangeable when reading a datasheet or nameplate is a common source of confusion.

9. Assuming any duty cycle is achievable on real hardware. Practical PWM drivers, relays, and gate drivers have minimum pulse-width and minimum dead-time limitations — a requested duty cycle translating to a pulse width shorter than the hardware can reliably produce (or a gap shorter than a mechanical relay can physically open/close within) may simply not be achieved as calculated, even though the arithmetic itself is valid.